Question

A space probe travels at a constant rate of 0.770c, starting from the Earth. The batteries in the probe power the transmitter that communicates with the Earth continuously. The batteries have a lifetime of 15.0 years as measured in the batteries’ rest frame.

a) How long does the power supply last as measured by Earth?

b) How far is the probe from the Earth when the batteries fail, as measured by Earth?

c) How far is the probe from the Earth according to the probe’s own measurements at this

time?

d) For what total time after launch does the Earth receive data from the probe? Keep in mind that the probe’s radio waves travel at the speed of light and fill the space between the probe and the Earth at the time the batteries fail.

Answer 1

a) use Time dialation equation,

T = To/sqrt(1 - (v/c)^2)

= 15.0/sqrt(1 - (0.77*c/c)^2)

= 15/sqrt(1 - 0.77^2)

= 23.5 years

b) The distnace between probe from the Earth when the batteries fail, as measured by Earth

d = v*T

= 0.77*c*23.5

= 18.09 light years

c) The distance between the probe from the Earth according to the probe’s own measurements at this time

d' = v*To

= 0.77*c*15

= 11.55 light years

d) time taken for the light waves to reach earth = d'/c

= 11.55 light years/c

= 11.55 years